After 1600yrs - 0.5 decayed, 0.5 left After 3200 yrs - there's 0.5 left, so you need to take half of that, i.e. a further 0.25 of the initial sample would have decayed. so total decayed = 0.75, total undecayed = 0.25 After 4800 - half of the 0.25 left will decayed, i.e. a further 0.125 of initial sample will decay. so total decayed = 0.75 + 0.125 = 0.875 of initial sample = 7/8 b) 6400 yrs is a further half life (from part a). After 4800 yrs, 1/8 is left, so after another half life, 1/16 will be left